Export from Blender to Maya preserving Materials and Crease
Unfortunately, FBX is the only serious option currently (maybe with Collada, but that format is not much supported/developed nowadays…).

FBX can support edge crease (LayerElementCrease node), just never had time/reasons to implement that in Blender. And I'd need a simple FBX file exported e.g. from Maya, with a dummy cube and various levels of crease on its edges, to be reasonably sure we do handle it correctly…

Besides that, afaik FBX does not support/have notion of groups of objects.

It should support reasonably simple rigging, but do not expect advanced stuff (like drivers, constraints, etc.) to survive, only basic bones skinned with basic vgroups.